Vorticity and Kutta Condition for Unsteady Multienergy Flows

1969 ◽  
Vol 36 (3) ◽  
pp. 608-613 ◽  
Author(s):  
J. P. Giesing
Keyword(s):  
Vortex Shedding ◽  
Pressure Difference ◽  
Total Pressure ◽  
Vortex Sheet ◽  
Rate Of Change ◽  
The Other ◽  
Numerical Calculations ◽  
Time Rate ◽  
Trailing Edge ◽  
Kutta Condition

The dynamical conditions for vortex shedding in unsteady multienergy flows are given: It is shown that the vorticity shed is composed of an unsteady part, which is proportional to the time rate of change of the circulation, and a steady part, which is proportional to the total-pressure difference across the vortex sheet. The kinematics of vortex shedding are also investigated. It is determined that the vortex sheet is shed parallel to one side of the trailing edge or the other depending on the sense of the shed vorticity. It is further determined that the shedding velocity is equal to one half of the strength of the vorticity at the trailing edge (except for trailing-edge angles of zero). Numerical calculations are presented to illustrate the results.

The influence of vortex shedding on the generation of sound by convected turbulence

1976 ◽  
Vol 76 (4) ◽  
pp. 711-740 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Vortex Shedding ◽  
Infinite Plate ◽  
Vortex Sheet ◽  
Realistic Model ◽  
Diffraction Field ◽  
Mean Flow ◽  
Turbulent Eddy ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Mathematical Problems

This paper discusses the theory of the generation of sound which occurs when a frozen turbulent eddy is convected in a mean flow past an airfoil or a semi-infinite plate, with and without the application of a Kutta condition and with and without the presence of a mean vortex sheet in the wake. A sequence of two-dimensional mathematical problems involving a prototype eddy in the form of a line vortex is examined, it being argued that this constitutes the simplest realistic model. Important effects of convection are deduced which hitherto have not been revealed by analyses which assume quadrupole sources to be at rest relative to the plate or airfoil. It is concluded that, to the order of approximation to which the sound from convected turbulence near a scattering body is usually estimated, the imposition of a Kutta condition at the trailing edge leads to a complete cancellation of the sound generated when frozen turbulence convects past a semi-infinite plate, and to the cancellation of the diffraction field produced by the trailing edge in the case of an airfoil of compact chord.

Sound diffraction at a trailing edge

1981 ◽  
Vol 108 ◽  
pp. 443-460 ◽  
Author(s):  
S. W. Rienstra
Keyword(s):  
Vortex Shedding ◽  
Pulse Wave ◽  
Layer Structure ◽  
Harmonic Wave ◽  
Sound Field ◽  
Edge Condition ◽  
Trailing Edge ◽  
Kutta Condition ◽  
High Reynolds ◽  
Sound Diffraction

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

Dynamic Analysis of Flexible Multi-Body Mechanical Systems

1996 ◽  
Vol 210 (4) ◽  
pp. 309-316
Author(s):  
P Davison ◽  
D K Longmore ◽  
C R Burrows
Keyword(s):  
Rate Of Change ◽  
The Other ◽  
Structural Deformation ◽  
Euler Parameters ◽  
Time Rate ◽  
Constraint Equations ◽  
Rigid Body Modes ◽  
The Individual ◽  
Multi Body ◽  
Flexible Component

The use of only the free component modes as coordinates when computing the motion of mechanisms involving flexible component structures connected together by driven or undriven joints has been further developed, with the constraint errors being controlled by penalty parameters related to both the errors and their time rate of change. Symbolic computation is used to incorporate the constraint equations into the solution program. The degenerate rigid-body modes may be indefinitely large, with Euler parameters being used for rotation, but the other free modes of the individual components, which involve structural deformation, are assumed small. The approach is examined in two examples in which the computed results are compared with experimental measurements.

Sound generation by a supersonic aerofoil cutting through a steady jet flow

1990 ◽  
Vol 216 ◽  
pp. 193-212 ◽  
Author(s):  
Y. P. Guo
Keyword(s):  
Vortex Shedding ◽  
Sound Field ◽  
Leading Edge ◽  
Jet Flow ◽  
Generation Process ◽  
Sound Waves ◽  
Leading Order ◽  
Sound Generation ◽  
Trailing Edge ◽  
Kutta Condition

This paper examines the sound generation process when a supersonic aerofoil cuts through a steady jet flow. It is shown that the principal sound is generated by the leading edge of the aerofoil when it interacts with the streaming jet. To the leading order in terms of the jet velocity, no trailing-edge sound is generated. This is not the result of the cancellation of a trailing-edge sound by that from vortex shedding through the imposition of the Kutta condition. Instead, the null acoustic radiation from the trailing edge is entirely because, to the leading order, there is no interaction between the trailing edge and the jet. The effect of the trailing edge is to diffract sound waves generated by the leading edge. It is shown that the diffracted field (as well as the incident field) is regular at the trailing edge and the issue of satisfying the Kutta condition does not arise during the diffraction process. Thus, there is no extra vortex shedding from the trailing edge owing to its interaction with the flow, apart from those resulting from the discontinuity across the aerofoil, generated by the flow-leading edge interaction. This is in sharp contrast to the case of subsonic aerofoils where the removal of the singularity in the diffracted field at the trailing edge through the imposition of the Kutta condition results in vortex shedding from the sharp edge and energy exchange between the sound field and the vortical wake.

scholarly journals Unsteady aerodynamics and vortex-sheet formation of a two-dimensional airfoil

2017 ◽  
Vol 830 ◽  
pp. 439-478 ◽  
Author(s):  
X. Xia ◽  
K. Mohseni
Keyword(s):  
Ad Hoc ◽  
Unsteady Aerodynamics ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
Formation Condition ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Flow Models ◽  
Edge Vortex

Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modelling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical steady Kutta condition can be extended to unsteady situations by realizing that a flow cannot turn abruptly around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a finite-angle trailing edge, or in the case of flow separation away from a sharp corner, the direction of the forming vortex sheet is ambiguous. To remove any ad hoc implementation, the unsteady Kutta condition, the conservation of circulation as well as the conservation laws of mass and momentum are coupled to analytically solve for the angle, strength and relative velocity of the trailing-edge vortex sheet. The two-dimensional aerodynamic model together with the proposed vortex-sheet formation condition is verified by comparing flow structures and force calculations with experimental results for several airfoil motions in steady and unsteady background flows.

The lift on an aerofoil in starting flow

1983 ◽  
Vol 133 ◽  
pp. 413-425 ◽  
Author(s):  
J. M. R. Graham
Keyword(s):  
Vortex Sheet ◽  
Sudden Onset ◽  
Rate Of Change ◽  
Impulsive Motion ◽  
Trailing Edge ◽  
Initial Development ◽  
Steady Rate ◽  
Spiral Shape ◽  
Lift And Drag ◽  
Starting Flow

An analysis is given of the initial development of the lift on an aerofoil in inviscid starting flow. It is shown that because of the spiral shape of the vortex sheet shed initially from the trailing edge the lift and drag are both singular at the start of impulsive motion. This result is in contrast with the prediction of finite forces by methods that assume the vortex sheet to be initially planar. The effect of a steady rate of change of incidence following the sudden onset of transverse (heaving) motion of an aerofoil in a steady stream is also discussed.

scholarly journals Note on the Physical Basis of the Kutta Condition in Unsteady Two-Dimensional Panel Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
M. La Mantia ◽  
P. Dabnichki
Keyword(s):  
Pressure Difference ◽  
Energy Requirements ◽  
Aquatic Species ◽  
Biological Applications ◽  
Velocity Difference ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Wing Motion ◽  
Panel Methods ◽  
New Formulation

Force generation in avian and aquatic species is of considerable interest for possible engineering applications. The aim of this work is to highlight the theoretical and physical foundations of a new formulation of the unsteady Kutta condition, which postulates a finite pressure difference at the trailing edge of the foil. The condition, necessary to obtain a unique solution and derived from the unsteady Bernoulli equation, implies that the energy supplied for the wing motion generates trailing-edge vortices and their overall effect, which depends on the motion initial parameters, is a jet of fluid that propels the wing. The postulated pressure difference (the value of which should be experimentally obtained) models the trailing-edge velocity difference that generates the thrust-producing jet. Although the average thrust values computed by the proposed method are comparable to those calculated by assuming null pressure difference at the trailing edge, the latter (commonly used) approach is less physically meaningful than the present one, as there is a singularity at the foil trailing edge. Additionally, in biological applications, that is, for autonomous flapping, the differences ought to be more significant, as the corresponding energy requirements should be substantially altered, compared to the studied oscillatory motions.

Direct Tail Actuation vs Internal Rotor Propulsion in Aquatic Robots

2017 ◽  
Author(s):  
Beau Pollard ◽  
Tyler Berkey ◽  
Phanindra Tallapragada
Keyword(s):  
Vortex Shedding ◽  
The Other ◽  
Trailing Edge ◽  
Internal Momentum ◽  
Aquatic Locomotion ◽  
Performance Differences ◽  
Tail Structure ◽  
Internal Rotor

It is common for scientists to look to nature for inspiration in developing robots. Many times biological creatures outperform even the best man made robots. We will be focusing on aquatic locomotion of robots inspired by the locomotion of fish. There are two different means of propulsion of the robots tested in this paper. One model of the robot is propelled only through the oscillations of an internal momentum wheel, while the other is propelled by the direct actuation of a tail structure. Both of these models achieve net propulsion through vortex shedding past their trailing edge, and two of the robots locomotion is also aided by the change in shape from either a passive or active tail. Tests were conducted to highlight the locomotion performance differences of the two different means of locomotion.

Some modeling issues on trailing-edge vortex shedding

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 787-793
Author(s):  
Wei Ning ◽  
Li He
Keyword(s):  
Vortex Shedding ◽  
Trailing Edge ◽  
Edge Vortex
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